Some combinations of anti-HIV drugs have been shown to reduce HIV in humans. The purposes of this study are to find out if treatment with certain drug combinations will decrease the amount of HIV in the blood and how long this decrease might last, to find out if the drug combinations can be safely given to children and adolescents who have advanced HIV disease or have not benefited from other HIV treatments, and to find the right doses of these drugs when the drugs are used in combination. The medications to be studied are zidovudine, didanosine, zalcitabine, stavudine, lamivudine, nevirapine, ritonavir, and nelfinavir.